Spectral analysis of convergence in slope-based wavefront reconstruction and a slow-subspace correction method

Slow convergence remains a major limitation in wavefront reconstruction from slope measurements, particularly for different aperture geometries and wavefront structures. This work shows that convergence behavior is governed by the alignment of the wavefront with a small set of slowly varying modes. A controlled overlap study establishes a direct causal link between the slow-mode content and convergence rate, and a weighted slow-mode overlap index is introduced as a practical indicator of reconstruction difficulty. A slow-subspace correction strategy is proposed to suppress these slowly decaying components during the iteration process. Numerical results demonstrate consistent acceleration across different apertures, with iteration reductions of five to seven times in challenging cases. Experimental validation using lateral shearing interferometry further shows that iteration counts are reduced from several thousand to fewer than 800–900, corresponding to approximately 8–10-fold acceleration and exceeding a 20-fold improvement for elliptical apertures.